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基于VO2和石墨烯实现hBN声子极化激元和自发发射率的主动调谐

周昆 马豪悦 孙希贤 吴小虎

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基于VO2和石墨烯实现hBN声子极化激元和自发发射率的主动调谐

周昆, 马豪悦, 孙希贤, 吴小虎

Active tuning hBN phonon polaritons and spontaneous emission rates based on VO2 and graphene

Zhou Kun, Ma Hao-Yue, Sun Xi-Xian, Wu Xiao-Hu
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  • 鉴于极化激元对介电环境异常敏感的特性, 本文中提出了双曲材料六方氮化硼(hBN)和石墨烯与相变材料二氧化钒(VO2)组成的异质结构, 用来研究hBN声子极化激元(PhPs)的主动可调谐性. 研究结果表明, 通过控制hBN/VO2异质结构中VO2相变可实现对hBN PhPs的主动调谐, 获得主动可调谐的自发发射(SE)率. 当在hBN/VO2异质结构中添加石墨烯时, 会在hBN双曲线带内耦合产生双曲等离子体-声子极化激元(HPPPs), 而在双曲线带外产生表面等离子体-声子极化激元(SPPPs), 通过控制VO2相态和调节石墨烯化学势亦可实现石墨烯/hBN/VO2异质结构的耦合色散及SE率的主动调谐. 该研究为使用诸如相变材料和石墨烯等功能材料调谐各向异性光学材料与光的相互作用机制提供了理论指导.
    Active tunability of phonon dispersion and spontaneous emission (SE) are still open problems due to their exciting potential applications. In view of the fact that polaritons are very sensitive to the dielectric environment, in this study, with the help of the differences in optical property between the phase change material vanadium dioxide (VO2) during the phase transition from the insulating state to metallic state and the tunable surface plasmon polaritons (SPPs) in graphene, a heterostructure composed of hyperbolic material hexagonal boron nitride (hBN) and graphene and VO2 is proposed to investigate the active tunability of hBN phonon polaritons (PhPs). In order to illustrate the underlying physical mechanism of the above heterostructures, the dispersion distributions of the above heterostructures are calculated and represented by the imaginary part of the p-polarized Fresnel reflection coefficient of the heterostructure, meanwhile the dispersion relation of the hBN/VO2 heterostructure in hyperbolic region is verified by the quasi-static approximation method.Results indicate that the active tunability of hBN PhPs inside type-I and type-II hyperbolic bands can be achieved by controlling VO2 phase transition in hBN/VO2 heterostructure. The PhP dispersion change of the hBN/VO2 heterostructure is mainly caused by the change of the VO2 dielectric function when VO2 substrate changes from the insulating state into metallic state, which affects the total Fresnel reflection coefficient of the heterostructure, finally resulting in the PhP dispersion change of hBN/VO2 heterostructure. When graphene is introduced into the hBN/VO2 heterostructure, coupled hyperbolic plasmon-phonon polaritons (HPPPs) are obtained within type-I and type-II hyperbolic band of hBN, while the surface plasmon-phonon polaritons (SPPPs) are generated outside its hyperbolic bands. Moreover, comparative analysis of SE rates is presented for a quantum emitter positioned with the hBN/VO2 and graphene/hBN/VO2 heterostructure, revealing that the SE rates of these heterostructures can be modulated by the passive means including changing the hBN thickness and distance between the dipole emitter and the proposed heterostructure, and also by the active means including tuning VO2 phase states and graphene chemical potential without changing structural configurations. This study provides a theoretical guidance in realizing active tunability of both phonon dispersion and SE rate of the natural or artificial anisotropic optical materials by using functional materials including phase change materials and graphene.
      通信作者: 周昆, zhoukun0209@163.com ; 吴小虎, xiaohu.wu@iat.cn
    • 基金项目: 国家自然科学基金(批准号: 52204258)、中央高校基本科研业务费专项资金(批准号: 2022QN1017)、新疆维吾尔自治区重点研发任务专项(批准号: 2022B03003-3)和山东省自然科学基金(批准号: ZR2022YQ57)资助的课题.
      Corresponding author: Zhou Kun, zhoukun0209@163.com ; Wu Xiao-Hu, xiaohu.wu@iat.cn
    • Funds: Project supported by National Natural Science Foundation of China (Grant No. 52204258), the Fundamental Research Funds for the Central Universities (Grant No. 2022QN1017), the Xinjiang Key Research and Development Special Task, China (Grant No. 2022B03003-3), and the Natural Science Foundation of Shandong Province, China (Grant No. ZR2022YQ57).
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    Drachev V P, Podolskiy V A, Kildishev A V 2013 Opt. Express 21 15048Google Scholar

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  • 图 1  (a) hBN/VO2异质结构示意图, t代表hBN的厚度; (b) VO2的折射系数n和消光系数k[15]; (c) hBN介电常数张量分量的实部

    Fig. 1.  (a) Schematic diagram of the hBN/VO2 heterostructure, t represents the hBN thickness; (b) the refractive index n and extinction coefficient k of VO2[15]; (c) real parts of the permittivity tensor components of hBN.

    图 2  (a) hBN/VO2(I)和 (b) hBN/VO2(M)异质结构的PhPs色散分布, 其中白色圆圈代表利用(4)式计算得到的色散分支; hBN/VO2异质结构在 (c) kx/k0 = 20和 (d) kx/k0 = 30的PhPs色散曲线

    Fig. 2.  (a) Hybrid PhPs dispersion of hBN/VO2(I) and (b) hBN/VO2(M) heterostructures, the white circles represent the dispersion branches calculated by Eq. (4); Dispersion curves of hBN/VO2 heterostructures at (c) kx/k0 = 20 and (d) kx/k0 = 30.

    图 3  (a)—(c)/(e)—(g) 石墨烯/hBN/VO2异质结构的耦合色散随石墨烯化学势μg的变化关系; (d) 石墨烯/hBN/VO2(I)异质结构在kx/k0 =20的色散曲线随石墨烯化学势μg的变化规律; (h) 石墨烯/hBN/VO2异质结构在kx/k0 = 20的色散曲线

    Fig. 3.  (a)–(c)/(e)–(g) Coupling dispersions of graphene/hBN/VO2 heterostructures as function of graphene chemical potentials μg; (d) dispersion curves of graphene/hBN/VO2(I) heterostructures at kx/k0 = 20 as function of graphene chemical potential μg; (h) dispersion curves of graphene/hBN/VO2 heterostructures at kx/k0 = 20.

    图 4  hBN/VO2异质结构在 (a) I和 (b) II型双曲线带内的SE率随hBN厚度t的变化规律

    Fig. 4.  SE rates of hBN/VO2 heterostructures within (a) type-I and (b) type-II hyperbolic bands as function of hBN thickness t.

    图 5  石墨烯/hBN/VO2异质结构在 (a) I和 (b) II双曲线带内的SE率随μg的变化规律. t = 90 nm

    Fig. 5.  SE rates of graphene/hBN/VO2 heterostructures within (a) type-I and (b) type-II hyperbolic bands as function of μg. t = 90 nm

  • [1]

    Poddubny A, Iorsh I, Belov P, Kivshar Y 2013 Nat. Photonics 7 948Google Scholar

    [2]

    Drachev V P, Podolskiy V A, Kildishev A V 2013 Opt. Express 21 15048Google Scholar

    [3]

    Wu X, McEleney C A, González-Jiménez M, Macêdo R 2019 Optica 6 1478Google Scholar

    [4]

    Zhou K, Lu L, Li B, Cheng Q 2021 J. Appl. Phys. 130 093102Google Scholar

    [5]

    Zhou C L, Zhang Y, Torbatian Z, Novko D, Antezza M 2022 Phys. Rev. Mater. 6 075201Google Scholar

    [6]

    刘伟, 黄勇, 吴会海 2017 工程热物理学报 38 2665

    Liu W, Huang Y, Wu H H 2017 J. Eng. Thermophys. 38 2665

    [7]

    Jiang H, Choudhury S, Kudyshev Z A, Wang D 2019 Photonics Res. 7 815Google Scholar

    [8]

    Zhang Q, Hu G, Ma W, Li P, Krasnok A, Hillenbrand R, Alù A 2021 Nature 597 187Google Scholar

    [9]

    Dai S, Zhang J, Ma Q, Kittiwatanakul S, McLeod A, Chen, X 2019 Adv. Mater. 31 1900251Google Scholar

    [10]

    Fei Z, Rodin A, Andreev G O 2012 Nature 487 82Google Scholar

    [11]

    Ju L, Geng B, Horng J 2011 Nat. Nanotechnol. 6 630Google Scholar

    [12]

    Zhou K, Cheng Q, Lu L 2020 Appl. Opt. 59 595Google Scholar

    [13]

    杨冲, 韩伟华, 陈俊东, 张晓迪, 郭仰岩 2020 微纳电子技术 57 341Google Scholar

    Yang C, Han W H, Chen J D, Zhang X D, Guo Y Y 2020 Micro-Nano Electron. Technol. 57 341Google Scholar

    [14]

    罗明海, 徐马记, 黄其伟, 李派, 何云斌 2016 物理学报 65 047201Google Scholar

    Luo M H, Xu M J, Huang Q W, Li P, He Y B 2016 Acta Phys. Sin. 65 047201Google Scholar

    [15]

    Benkahoul M, Chaker M, Margot J 2011 Sol. Energy Mater. Sol. Cells. 95 3504Google Scholar

    [16]

    赵海鹏, 章新源, 何云斌, 豆书亮, 李垚, 李孝峰, 詹耀辉 2021 光学学报 41 1523001

    Zhao H P, Z X Y, He Y B, Dou S L, Li Y, Li X F, Zhan Y H 2021 Acta Opt. Sin. 41 1523001 (in Chinese)

    [17]

    Soltani M, Chaker M, Haddad E 2004 Appl. Phys. Lett. 85 1958Google Scholar

    [18]

    Lee S, Hippalgaonkar K, Yang F 2017 Science 355 371Google Scholar

    [19]

    Tang K, Dong K, Li J 2021 Science 374 1504Google Scholar

    [20]

    黄雅琴, 李毅, 李政鹏, 裴江恒, 田蓉, 刘进, 周建忠, 方宝英, 王晓华, 肖寒 2019 光学学报 39 0316001Google Scholar

    Huang Y Q, Li Y, Li Z P, Pei J H, Tian R, Liu J, Zhou J Z, Fang B Y, Wang X H, Xiao H 2019 Acta Optics Sinica 39 0316001Google Scholar

    [21]

    Mlyuka N, Niklasson G A, Granqvist C-G 2009 Sol. Energy Mater. Sol. Cells. 93 1685Google Scholar

    [22]

    Kumar A, Low T, Fung K H 2015 Nano Lett. 15 3172Google Scholar

    [23]

    Zhou K, Cheng Q, Lu L 2020 Opt. Express 28 1647Google Scholar

    [24]

    Zhou K, Cheng Q, Song J 2019 Opt. Lett. 44 3430Google Scholar

    [25]

    Dai S, Ma Q, Andersen T, Mcleod A S, Fei Z, Liu M K, Wagner M, Watanabe K, Taniguchi T, Thiemens M, Keilmann F, Jarillo-Herrero P, Fogler M M, Basov D N 2015 Nat. Commun. 6 6963Google Scholar

    [26]

    Debu D T, Ladani F T, French D 2019 npj 2D Mater. Appl. 3 1Google Scholar

    [27]

    Álvarez‐Pérez G, Folland T G, Errea I 2020 Adv. Mater. 32 1908176Google Scholar

    [28]

    Zhao B, Guizal B, Zhang Z M 2017 Phys. Rev. B 95 246437Google Scholar

    [29]

    Purcell E M, Torrey H C, Pound R V 1946 Phys. Rev. 69 37Google Scholar

    [30]

    赵永生, 宋俊峰, 韩伟华, 李雪梅, 杜国同, 高鼎三 1999 光学学报 19 452Google Scholar

    Zhao Y S, Song J F, Han W H, Li X M, Du G T, Gao D S 1999 Acta Optics Sinica. 19 452Google Scholar

    [31]

    Cortes C, Newman W, Molesky S 2012 J. Opt. 14 063001Google Scholar

    [32]

    Krishnamoorthy H N, Jacob Z, Narimanov E 2012 Science 336 205Google Scholar

    [33]

    Zhou K, Zhong X, Cheng Q, Wu X 2022 Opt. Mater. 131 112623Google Scholar

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  • 收稿日期:  2022-11-12
  • 修回日期:  2022-12-31
  • 上网日期:  2023-02-04
  • 刊出日期:  2023-04-05

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